In an apocalyptic winter filled with zombies, Juliet is on a rampage to kill Romeo at all costs.

The last draft of the logline reads better and adds clarity over the original one. Most loglines don't include character names so don't feel bad about omitting them. The only reason to include a character name is if the name informs nature of the character in a story critical way such as Jesus or Gandhi?

In this instance as previously mentioned the names are not fulfilling that role.

I would drop the left for dead betrayed by her true love is enough for an inciting incident. I would also change the character description to reflect more about the Mc nature and flaw than "...one woman?".

After she is betrayed by her true love during a zombie apocalypse a shy librarian must take up arms to exact revenge against her fianc?.

I would add perhaps that she must lead a group of patrons to freedom in to the mix or other wise give her an additional hurdle to over come.

Alright. I'm clearly outnumbered. While I do put those themes in the script, the themes would not be shown in a Wikipedia synopsis, or at leastvery little would so to speak. Looking through it again I see it more than I feel an audience would. So instead I should write; "After being betrayed by her true love and left for dead in a jail cel in an apocalyptic winter filled with zombies, one woman goes on a war path to exact revenge against the man that betrayed her."
Feels goofy without names but this probably send the message clearer

If you use their names, there is no way readers are not going to associate your story with Shakespeare's play. As I certainly did . This raises certain expectations as to what your story is about. And then when you say the semblance to Shakespeare's play is only 'superficial' -- well, now I'm really confused. Now your logline creates the impression of a bait and switch. Which, of course, is not your intention. So, yeah, it's probably better to drop the names.

Finally, what makes Shakespeare's play a classic is that it is about a universal theme -- love, specifically about love arising in the context of hate. The theme and resulting conflict has universal appeal -- it's something people can identify and empathize with across all cultures and all time. More important than whether your story has any semblance to the play is whether, like Shakespeare, you are writing about a universal theme, a universal human predicament.